Recent Advances in Operator Theory in Hilbert and Krein Spaces

The present book is a memorial volume devoted to Peter Jonas. It displays recent advances in modern operator theory in Hilbert and Krein spaces and contains a collection of original research papers written by many well-known specialists in this field. The papers contain new results for problems close to the area of research of Peter Jonas: Spectral and perturbation problems for operators in inner product spaces, generalized Nevanlinna functions and definitizable functions, scattering theory, extension theory for symmetric operators, fixed points, hyperbolic matrix polynomials, moment problems, indefinite spectral and Sturm-Liouville problems, and invariant subspace problems.

This book is written for researchers and postgraduates interested in functional analysis and differential operators.

Local Scattering Problem and a Solvable Model of Quantum Network.- Quadratic (Weakly) Hyperbolic Matrix Polynomials: Direct and Inverse Spectral Problems.- A Theorem on Existence of Invariant Subspaces for J-binoncontractive Operators.- Moment Problems for Real Measures on the Unit Circle.- Finite Rank Perturbations, Scattering Matrices and Inverse Problems.- Conditions for an Indefinite Sturm-Liouville Riesz Basis Property.- Convergence of Diagonal Padé Approximants for a Class of Definitizable Functions.- Approximation of N ? ? -functions II: Convergence of Models.- Nonnegative Extensions via Embeddings.- Fredholm Properties of Unbounded Operators on Interpolation Spaces.- Domain and Range Descriptions for Adjoint Relations, and Parallel Sums and Differences of Forms.- The Königs Problem and Extreme Fixed Points.- Bisectors, Isometries and Connected Components in Hilbert Spaces.- On Norms in Indefinite Inner Product Spaces.- Interpolation of Sobolev Spaces and Indefinite Elliptic Spectral Problems.- On the Spectrum of a Quantum Dot with Impurity in the Lobachevsky Plane.- Note on Interlacing for Hyperbolic Quadratic Pencils.